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Simplifying x(5x + 16) = 2x2 + -9x + 18 Reorder the terms: x(16 + 5x) = 2x2 + -9x + 18 (16 * x + 5x * x) = 2x2 + -9x + 18 (16x + 5x2) = 2x2 + -9x + 18 Reorder the terms: 16x + 5x2 = 18 + -9x + 2x2 Solving 16x + 5x2 = 18 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: -18 + 16x + 9x + 5x2 + -2x2 = 18 + -9x + 2x2 + -18 + 9x + -2x2 Combine like terms: 16x + 9x = 25x -18 + 25x + 5x2 + -2x2 = 18 + -9x + 2x2 + -18 + 9x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -18 + 25x + 3x2 = 18 + -9x + 2x2 + -18 + 9x + -2x2 Reorder the terms: -18 + 25x + 3x2 = 18 + -18 + -9x + 9x + 2x2 + -2x2 Combine like terms: 18 + -18 = 0 -18 + 25x + 3x2 = 0 + -9x + 9x + 2x2 + -2x2 -18 + 25x + 3x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 -18 + 25x + 3x2 = 0 + 2x2 + -2x2 -18 + 25x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -18 + 25x + 3x2 = 0 Factor a trinomial. (-9 + -1x)(2 + -3x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-9, 0.6666666667}
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